// SPDX-License-Identifier: GPL-2.0
/*
 * kernel/sched/loadavg.c
 *
 * This file contains the magic bits required to compute the global loadavg
 * figure. Its a silly number but people think its important. We go through
 * great pains to make it work on big machines and tickless kernels.
 */
#include "sched.h"

/*
 * Global load-average calculations
 *
 * We take a distributed and async approach to calculating the global load-avg
 * in order to minimize overhead.
 *
 * The global load average is an exponentially decaying average of nr_running +
 * nr_uninterruptible.
 *
 * Once every LOAD_FREQ:
 *
 *   nr_active = 0;
 *   for_each_possible_cpu(cpu)
 *	nr_active += cpu_of(cpu)->nr_running + cpu_of(cpu)->nr_uninterruptible;
 *
 *   avenrun[n] = avenrun[0] * exp_n + nr_active * (1 - exp_n)
 *
 * Due to a number of reasons the above turns in the mess below:
 *
 *  - for_each_possible_cpu() is prohibitively expensive on machines with
 *    serious number of CPUs, therefore we need to take a distributed approach
 *    to calculating nr_active.
 *
 *        \Sum_i x_i(t) = \Sum_i x_i(t) - x_i(t_0) | x_i(t_0) := 0
 *                      = \Sum_i { \Sum_j=1 x_i(t_j) - x_i(t_j-1) }
 *
 *    So assuming nr_active := 0 when we start out -- true per definition, we
 *    can simply take per-CPU deltas and fold those into a global accumulate
 *    to obtain the same result. See calc_load_fold_active().
 *
 *    Furthermore, in order to avoid synchronizing all per-CPU delta folding
 *    across the machine, we assume 10 ticks is sufficient time for every
 *    CPU to have completed this task.
 *
 *    This places an upper-bound on the IRQ-off latency of the machine. Then
 *    again, being late doesn't loose the delta, just wrecks the sample.
 *
 *  - cpu_rq()->nr_uninterruptible isn't accurately tracked per-CPU because
 *    this would add another cross-CPU cacheline miss and atomic operation
 *    to the wakeup path. Instead we increment on whatever CPU the task ran
 *    when it went into uninterruptible state and decrement on whatever CPU
 *    did the wakeup. This means that only the sum of nr_uninterruptible over
 *    all CPUs yields the correct result.
 *
 *  This covers the NO_HZ=n code, for extra head-aches, see the comment below.
 */

/* Variables and functions for calc_load */
static atomic_long_t calc_load_tasks;
unsigned long calc_load_update;
unsigned long avenrun[3];

/**
 * get_avenrun - get the load average array
 * @loads:	pointer to dest load array
 * @offset:	offset to add
 * @shift:	shift count to shift the result left
 *
 * These values are estimates at best, so no need for locking.
 */
void get_avenrun(unsigned long *loads, unsigned long offset, int shift)
{
    loads[0] = (avenrun[0] + offset) << shift;
    loads[1] = (avenrun[1] + offset) << shift;
    loads[2] = (avenrun[2] + offset) << shift;
}

static long calc_load_fold_active(struct rq *this_rq, long adjust)
{
    long nr_active, delta = 0;

    nr_active = this_rq->nr_running - adjust;
    nr_active += (long)this_rq->nr_uninterruptible;

    if (nr_active != this_rq->calc_load_active) {
        delta = nr_active - this_rq->calc_load_active;
        this_rq->calc_load_active = nr_active;
    }

    return delta;
}

/**
 * fixed_power_int - compute: x^n, in O(log n) time
 *
 * @x:         base of the power
 * @frac_bits: fractional bits of @x
 * @n:         power to raise @x to.
 *
 * By exploiting the relation between the definition of the natural power
 * function: x^n := x*x*...*x (x multiplied by itself for n times), and
 * the binary encoding of numbers used by computers: n := \Sum n_i * 2^i,
 * (where: n_i \elem {0, 1}, the binary vector representing n),
 * we find: x^n := x^(\Sum n_i * 2^i) := \Prod x^(n_i * 2^i), which is
 * of course trivially computable in O(log_2 n), the length of our binary
 * vector.
 */
static unsigned long
fixed_power_int(unsigned long x, unsigned int frac_bits, unsigned int n)
{
    unsigned long result = 1UL << frac_bits;

    if (n) {
        for (;;) {
            if (n & 1) {
                result *= x;
                result += 1UL << (frac_bits - 1);
                result >>= frac_bits;
            }
            n >>= 1;
            if (!n)
                break;
            x *= x;
            x += 1UL << (frac_bits - 1);
            x >>= frac_bits;
        }
    }

    return result;
}

/*
 * a1 = a0 * e + a * (1 - e)
 *
 * a2 = a1 * e + a * (1 - e)
 *    = (a0 * e + a * (1 - e)) * e + a * (1 - e)
 *    = a0 * e^2 + a * (1 - e) * (1 + e)
 *
 * a3 = a2 * e + a * (1 - e)
 *    = (a0 * e^2 + a * (1 - e) * (1 + e)) * e + a * (1 - e)
 *    = a0 * e^3 + a * (1 - e) * (1 + e + e^2)
 *
 *  ...
 *
 * an = a0 * e^n + a * (1 - e) * (1 + e + ... + e^n-1) [1]
 *    = a0 * e^n + a * (1 - e) * (1 - e^n)/(1 - e)
 *    = a0 * e^n + a * (1 - e^n)
 *
 * [1] application of the geometric series:
 *
 *              n         1 - x^(n+1)
 *     S_n := \Sum x^i = -------------
 *             i=0          1 - x
 */
static unsigned long
calc_load_n(unsigned long load, unsigned long exp,
        unsigned long active, unsigned int n)
{
    return calc_load(load, fixed_power_int(exp, FSHIFT, n), active);
}

/*
 * Handle NO_HZ for the global load-average.
 *
 * Since the above described distributed algorithm to compute the global
 * load-average relies on per-CPU sampling from the tick, it is affected by
 * NO_HZ.
 *
 * The basic idea is to fold the nr_active delta into a global NO_HZ-delta upon
 * entering NO_HZ state such that we can include this as an 'extra' CPU delta
 * when we read the global state.
 *
 * Obviously reality has to ruin such a delightfully simple scheme:
 *
 *  - When we go NO_HZ idle during the window, we can negate our sample
 *    contribution, causing under-accounting.
 *
 *    We avoid this by keeping two NO_HZ-delta counters and flipping them
 *    when the window starts, thus separating old and new NO_HZ load.
 *
 *    The only trick is the slight shift in index flip for read vs write.
 *
 *        0s            5s            10s           15s
 *          +10           +10           +10           +10
 *        |-|-----------|-|-----------|-|-----------|-|
 *    r:0 0 1           1 0           0 1           1 0
 *    w:0 1 1           0 0           1 1           0 0
 *
 *    This ensures we'll fold the old NO_HZ contribution in this window while
 *    accumlating the new one.
 *
 *  - When we wake up from NO_HZ during the window, we push up our
 *    contribution, since we effectively move our sample point to a known
 *    busy state.
 *
 *    This is solved by pushing the window forward, and thus skipping the
 *    sample, for this CPU (effectively using the NO_HZ-delta for this CPU which
 *    was in effect at the time the window opened). This also solves the issue
 *    of having to deal with a CPU having been in NO_HZ for multiple LOAD_FREQ
 *    intervals.
 *
 * When making the ILB scale, we should try to pull this in as well.
 */
static atomic_long_t calc_load_nohz[2];
static int calc_load_idx;

static inline int calc_load_write_idx(void)
{
    int idx = calc_load_idx;

    /*
     * See calc_global_nohz(), if we observe the new index, we also
     * need to observe the new update time.
     */
    smp_rmb();

    /*
     * If the folding window started, make sure we start writing in the
     * next NO_HZ-delta.
     */
    if (!time_before((unsigned long)jiffies_64, READ_ONCE(calc_load_update)))
        idx++;

    return idx & 1;
}

static inline int calc_load_read_idx(void)
{
    return calc_load_idx & 1;
}

static long calc_load_nohz_fold(void)
{
    int idx = calc_load_read_idx();
    long delta = 0;

    if (atomic_long_read(&calc_load_nohz[idx]))
        delta = atomic_long_xchg(&calc_load_nohz[idx], 0);

    return delta;
}

/*
 * NO_HZ can leave us missing all per-CPU ticks calling
 * calc_load_fold_active(), but since a NO_HZ CPU folds its delta into
 * calc_load_nohz per calc_load_nohz_start(), all we need to do is fold
 * in the pending NO_HZ delta if our NO_HZ period crossed a load cycle boundary.
 *
 * Once we've updated the global active value, we need to apply the exponential
 * weights adjusted to the number of cycles missed.
 */
static void calc_global_nohz(void)
{
    unsigned long sample_window;
    long delta, active, n;

    sample_window = READ_ONCE(calc_load_update);
    if (!time_before((unsigned long)jiffies_64, sample_window + 10)) {
        /*
         * Catch-up, fold however many we are behind still
         */
        delta = jiffies_64 - sample_window - 10;
        n = 1 + (delta / LOAD_FREQ);

        active = atomic_long_read(&calc_load_tasks);
        active = active > 0 ? active * FIXED_1 : 0;

        avenrun[0] = calc_load_n(avenrun[0], EXP_1, active, n);
        avenrun[1] = calc_load_n(avenrun[1], EXP_5, active, n);
        avenrun[2] = calc_load_n(avenrun[2], EXP_15, active, n);

        WRITE_ONCE(calc_load_update, sample_window + n * LOAD_FREQ);
    }

    /*
     * Flip the NO_HZ index...
     *
     * Make sure we first write the new time then flip the index, so that
     * calc_load_write_idx() will see the new time when it reads the new
     * index, this avoids a double flip messing things up.
     */
    smp_wmb();
    calc_load_idx++;
}

/*
 * calc_load - update the avenrun load estimates 10 ticks after the
 * CPUs have updated calc_load_tasks.
 *
 * Called from the global timer code.
 */
void calc_global_load(unsigned long ticks)
{
    unsigned long sample_window;
    long active, delta;

    sample_window = READ_ONCE(calc_load_update);
    if (time_before((unsigned long)jiffies_64, (sample_window + 10)))
        return;

    /*
     * Fold the 'old' NO_HZ-delta to include all NO_HZ CPUs.
     */
    delta = calc_load_nohz_fold();
    if (delta)
        atomic_long_add(delta, &calc_load_tasks);

    active = atomic_long_read(&calc_load_tasks);
    active = active > 0 ? active * FIXED_1 : 0;

    avenrun[0] = calc_load(avenrun[0], EXP_1, active);
    avenrun[1] = calc_load(avenrun[1], EXP_5, active);
    avenrun[2] = calc_load(avenrun[2], EXP_15, active);

    WRITE_ONCE(calc_load_update, sample_window + LOAD_FREQ);

    /*
     * In case we went to NO_HZ for multiple LOAD_FREQ intervals
     * catch up in bulk.
     */
    calc_global_nohz();
}

/*
 * Called from scheduler_tick() to periodically update this CPU's
 * active count.
 */
void calc_global_load_tick(struct rq *this_rq)
{
    long delta;

    if (time_before((unsigned long)jiffies_64, this_rq->calc_load_update))
        return;

    delta  = calc_load_fold_active(this_rq, 0);
    if (delta)
        atomic_long_add(delta, &calc_load_tasks);

    this_rq->calc_load_update += LOAD_FREQ;
}
